(x+iy)/(1+(x-iy))=3+4i

解答

\frac{x + i y}{1 + ( x - i y )} = 3 + 4 i

x = - \frac{7}{6}, y = - \frac{1}{6}

求解步骤

\frac{x + i y}{1 + ( x - i y )} = 3 + 4 i

在两边乘以

1 + x - i y

\frac{x + i y}{1 + x - i y} (1 + x - i y) = 3 (1 + x - i y) + 4 i (1 + x - i y)

乘开

x + i y = (3 + 3 x + 4 y) + i (4 - 3 y + 4 x)

复数仅在实部和虚部均相等时才相等改写为方程组:

[x = 3 + 3 x + 4 y y = 4 - 3 y + 4 x]

[x = 3 + 3 x + 4 y y = 4 - 3 y + 4 x] : x = - \frac{7}{6}, y = - \frac{1}{6}

x = - \frac{7}{6}, y = - \frac{1}{6}

(i - 5) z + (i - 2) z^{2} + 2 - 2 i = 0

z - \frac{1}{z} = 3 + 4 i

i (x) = ∣ 2 y + 5 ∣

so l v e f or m, y = (x - 3)^{2} minim o

so l v e f or z, \frac{z}{1 - z} = 1 - 5 i